---
_id: '4491'
abstract:
- lang: eng
text: We present two methods for translating nonlinear hybrid systems into linear
hybrid automata. Properties of the nonlinear systems can then be inferred from
the automatic analysis of the translated linear hybrid automata. The first method,
called clock translation, replaces constraints on nonlinear variables by constraints
on clock variables. The second method, called linear phase-portrait approximation,
conservatively overapproximates the phase portrait of a hybrid automaton using
piecewise-constant polyhedral differential inclusions. Both methods are sound
for safety properties. We illustrate both methods by using HYTECH, a symbolic
model checker for linear hybrid automata, to automatically check properties of
a nonlinear temperature controller and of a predator-prey ecology
article_processing_charge: No
article_type: original
author:
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
- first_name: Pei
full_name: Ho, Pei
last_name: Ho
- first_name: Howard
full_name: Wong Toi, Howard
last_name: Wong Toi
citation:
ama: Henzinger TA, Ho P, Wong Toi H. Algorithmic analysis of nonlinear hybrid systems.
IEEE Transactions on Automatic Control. 1998;43(4):540-554. doi:10.1109/9.664156
apa: Henzinger, T. A., Ho, P., & Wong Toi, H. (1998). Algorithmic analysis of
nonlinear hybrid systems. IEEE Transactions on Automatic Control. IEEE.
https://doi.org/10.1109/9.664156
chicago: Henzinger, Thomas A, Pei Ho, and Howard Wong Toi. “Algorithmic Analysis
of Nonlinear Hybrid Systems.” IEEE Transactions on Automatic Control. IEEE,
1998. https://doi.org/10.1109/9.664156
.
ieee: T. A. Henzinger, P. Ho, and H. Wong Toi, “Algorithmic analysis of nonlinear
hybrid systems,” IEEE Transactions on Automatic Control, vol. 43, no. 4.
IEEE, pp. 540–554, 1998.
ista: Henzinger TA, Ho P, Wong Toi H. 1998. Algorithmic analysis of nonlinear hybrid
systems. IEEE Transactions on Automatic Control. 43(4), 540–554.
mla: Henzinger, Thomas A., et al. “Algorithmic Analysis of Nonlinear Hybrid Systems.”
IEEE Transactions on Automatic Control, vol. 43, no. 4, IEEE, 1998, pp.
540–54, doi:10.1109/9.664156 .
short: T.A. Henzinger, P. Ho, H. Wong Toi, IEEE Transactions on Automatic Control
43 (1998) 540–554.
date_created: 2018-12-11T12:09:07Z
date_published: 1998-01-01T00:00:00Z
date_updated: 2022-08-23T14:34:35Z
day: '01'
doi: '10.1109/9.664156 '
extern: '1'
intvolume: ' 43'
issue: '4'
language:
- iso: eng
month: '01'
oa_version: None
page: 540 - 554
publication: IEEE Transactions on Automatic Control
publication_identifier:
issn:
- 0018-9162
publication_status: published
publisher: IEEE
publist_id: '238'
quality_controlled: '1'
status: public
title: Algorithmic analysis of nonlinear hybrid systems
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 43
year: '1998'
...
---
_id: '4611'
abstract:
- lang: eng
text: Presents a model-checking procedure and its implementation for the automatic
verification of embedded systems. The system components are described as hybrid
automata-communicating machines with finite control and real-valued variables
that represent continuous environment parameters such as time, pressure and temperature.
The system requirements are specified in a temporal logic with stop-watches, and
verified by symbolic fixpoint computation. The verification procedure-implemented
in the Cornell Hybrid Technology tool, HyTech-applies to hybrid automata whose
continuous dynamics is governed by linear constraints on the variables and their
derivatives. We illustrate the method and the tool by checking safety, liveness,
time-bounded and duration requirements of digital controllers, schedulers and
distributed algorithms
acknowledgement: "We thank Costas Courcoubetis, Nicolas Halbwachs, Peter Kopke, Joseph
Sifakis, and Howard Wong-Toi for helpful\r\ndiscussions and valuable comments. Thomas
A. Henzinger's research was supported in part by the U.S. Office of Naval Research
Young Investigator award N00014-95-1-0520, by the National Science Foundation CAREER
award CCR-9501708, by National Science Foundation grants CCR-9200794 and CCR-9504469,
by U.S. Air Force Office of Scientific Research contract F49620-93-1- 0056, and
by Advanced Research Projects Agency grant NAG2-892. "
article_processing_charge: No
article_type: original
author:
- first_name: Rajeev
full_name: Alur, Rajeev
last_name: Alur
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
- first_name: Pei
full_name: Ho, Pei
last_name: Ho
citation:
ama: Alur R, Henzinger TA, Ho P. Automatic symbolic verification of embedded systems.
IEEE Transactions on Software Engineering. 1996;22(3):181-201. doi:10.1109/32.489079
apa: Alur, R., Henzinger, T. A., & Ho, P. (1996). Automatic symbolic verification
of embedded systems. IEEE Transactions on Software Engineering. IEEE. https://doi.org/10.1109/32.489079
chicago: Alur, Rajeev, Thomas A Henzinger, and Pei Ho. “Automatic Symbolic Verification
of Embedded Systems.” IEEE Transactions on Software Engineering. IEEE,
1996. https://doi.org/10.1109/32.489079.
ieee: R. Alur, T. A. Henzinger, and P. Ho, “Automatic symbolic verification of embedded
systems,” IEEE Transactions on Software Engineering, vol. 22, no. 3. IEEE,
pp. 181–201, 1996.
ista: Alur R, Henzinger TA, Ho P. 1996. Automatic symbolic verification of embedded
systems. IEEE Transactions on Software Engineering. 22(3), 181–201.
mla: Alur, Rajeev, et al. “Automatic Symbolic Verification of Embedded Systems.”
IEEE Transactions on Software Engineering, vol. 22, no. 3, IEEE, 1996,
pp. 181–201, doi:10.1109/32.489079.
short: R. Alur, T.A. Henzinger, P. Ho, IEEE Transactions on Software Engineering
22 (1996) 181–201.
date_created: 2018-12-11T12:09:45Z
date_published: 1996-03-01T00:00:00Z
date_updated: 2022-07-04T12:47:05Z
day: '01'
doi: 10.1109/32.489079
extern: '1'
intvolume: ' 22'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://ecommons.cornell.edu/handle/1813/7170
month: '03'
oa: 1
oa_version: Published Version
page: 181 - 201
publication: IEEE Transactions on Software Engineering
publication_identifier:
issn:
- 0018-9162
publication_status: published
publisher: IEEE
publist_id: '96'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Automatic symbolic verification of embedded systems
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 22
year: '1996'
...
---
_id: '4024'
abstract:
- lang: eng
text: We have developed general modeling software for a Cave Automatic Virtual Environment
(CAVE); one of its applications is modeling 3D protein structures, generating
both outside-in and inside-out views of geometric models. An advantage of the
CAVE over other virtual environments is that multiple viewers can observe the
same scene at the same time and place. Our software is scalable-from high-end
virtual environments such as the CAVE, to mid-range immersive desktop systems,
down to low-end graphics workstations. In the current configuration, a parallel
Silicon Graphics Power Challenge supercomputer architecture performs the computationally
intensive construction of surface patches remotely, and sends the results through
the I-WAY (Information Wide Area Year) using VBNS (Very-high-Bandwidth Network
Systems) to the graphics machines that drive the CAVE and our graphics visualization
software, Valvis (Virtual ALpha shapes VISualizer).
article_processing_charge: No
article_type: original
author:
- first_name: Nataraj
full_name: Akkiraju, Nataraj
last_name: Akkiraju
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Ping
full_name: Fu, Ping
last_name: Fu
- first_name: Jiang
full_name: Qian, Jiang
last_name: Qian
citation:
ama: Akkiraju N, Edelsbrunner H, Fu P, Qian J. Viewing geometric protein structures
from inside a CAVE. IEEE Computer Graphics and Applications. 1996;16(4):58-61.
doi:10.1109/38.511855
apa: Akkiraju, N., Edelsbrunner, H., Fu, P., & Qian, J. (1996). Viewing geometric
protein structures from inside a CAVE. IEEE Computer Graphics and Applications.
IEEE. https://doi.org/10.1109/38.511855
chicago: Akkiraju, Nataraj, Herbert Edelsbrunner, Ping Fu, and Jiang Qian. “Viewing
Geometric Protein Structures from inside a CAVE.” IEEE Computer Graphics and
Applications. IEEE, 1996. https://doi.org/10.1109/38.511855.
ieee: N. Akkiraju, H. Edelsbrunner, P. Fu, and J. Qian, “Viewing geometric protein
structures from inside a CAVE,” IEEE Computer Graphics and Applications,
vol. 16, no. 4. IEEE, pp. 58–61, 1996.
ista: Akkiraju N, Edelsbrunner H, Fu P, Qian J. 1996. Viewing geometric protein
structures from inside a CAVE. IEEE Computer Graphics and Applications. 16(4),
58–61.
mla: Akkiraju, Nataraj, et al. “Viewing Geometric Protein Structures from inside
a CAVE.” IEEE Computer Graphics and Applications, vol. 16, no. 4, IEEE,
1996, pp. 58–61, doi:10.1109/38.511855.
short: N. Akkiraju, H. Edelsbrunner, P. Fu, J. Qian, IEEE Computer Graphics and
Applications 16 (1996) 58–61.
date_created: 2018-12-11T12:06:30Z
date_published: 1996-07-01T00:00:00Z
date_updated: 2022-08-09T13:32:21Z
day: '01'
doi: 10.1109/38.511855
extern: '1'
intvolume: ' 16'
issue: '4'
language:
- iso: eng
month: '07'
oa_version: None
page: 58 - 61
publication: IEEE Computer Graphics and Applications
publication_identifier:
issn:
- 0018-9162
publication_status: published
publisher: IEEE
publist_id: '2101'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Viewing geometric protein structures from inside a CAVE
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 16
year: '1996'
...
---
_id: '4588'
abstract:
- lang: eng
text: 'We present a formal model for concurrent systems. The model represents synchronous
and asynchronous components in a uniform framework that supports compositional
(assume-guarantee) and hierarchical (stepwise refinement) reasoning. While synchronous
models are based on a notion of atomic computation step, and asynchronous models
remove that notion by introducing stuttering, our model is based on a flexible
notion of what constitutes a computation step: by applying an abstraction operator
to a system, arbitrarily many consecutive steps can be collapsed into a single
step. The abstraction operator, which may turn an asynchronous system into a synchronous
one, allows us to describe systems at various levels of temporal detail. For describing
systems at various levels of spatial detail, we use a hiding operator that may
turn a synchronous system into an asynchronous one. We illustrate the model with
diverse examples from synchronous circuits, asynchronous shared-memory programs,
and synchronous message passing'
article_processing_charge: No
author:
- first_name: Rajeev
full_name: Alur, Rajeev
last_name: Alur
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
citation:
ama: 'Alur R, Henzinger TA. Reactive modules. In: Proceedings 11th Annual IEEE
Symposium on Logic in Computer Science. IEEE; 1996:207-218. doi:10.1109/LICS.1996.561320'
apa: 'Alur, R., & Henzinger, T. A. (1996). Reactive modules. In Proceedings
11th Annual IEEE Symposium on Logic in Computer Science (pp. 207–218). New
Brunswick, NJ, USA: IEEE. https://doi.org/10.1109/LICS.1996.561320'
chicago: Alur, Rajeev, and Thomas A Henzinger. “Reactive Modules.” In Proceedings
11th Annual IEEE Symposium on Logic in Computer Science, 207–18. IEEE, 1996.
https://doi.org/10.1109/LICS.1996.561320.
ieee: R. Alur and T. A. Henzinger, “Reactive modules,” in Proceedings 11th Annual
IEEE Symposium on Logic in Computer Science, New Brunswick, NJ, USA, 1996,
pp. 207–218.
ista: 'Alur R, Henzinger TA. 1996. Reactive modules. Proceedings 11th Annual IEEE
Symposium on Logic in Computer Science. LICS: Logic in Computer Science, 207–218.'
mla: Alur, Rajeev, and Thomas A. Henzinger. “Reactive Modules.” Proceedings 11th
Annual IEEE Symposium on Logic in Computer Science, IEEE, 1996, pp. 207–18,
doi:10.1109/LICS.1996.561320.
short: R. Alur, T.A. Henzinger, in:, Proceedings 11th Annual IEEE Symposium on Logic
in Computer Science, IEEE, 1996, pp. 207–218.
conference:
end_date: 1996-07-30
location: New Brunswick, NJ, USA
name: 'LICS: Logic in Computer Science'
start_date: 1996-07-27
date_created: 2018-12-11T12:09:37Z
date_published: 1996-01-01T00:00:00Z
date_updated: 2022-07-04T14:51:40Z
day: '01'
doi: 10.1109/LICS.1996.561320
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://ieeexplore.ieee.org/document/561320
month: '01'
oa_version: None
page: 207 - 218
publication: Proceedings 11th Annual IEEE Symposium on Logic in Computer Science
publication_identifier:
issn:
- 0018-9162
publication_status: published
publisher: IEEE
publist_id: '121'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Reactive modules
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
year: '1996'
...
---
_id: '4586'
abstract:
- lang: eng
text: 'Fairness is a mathematical abstraction: in a multiprogramming environment,
fairness abstracts the details of admissible (“fair”) schedulers; in a distributed
environment, fairness abstracts the speeds of independent processors. We argue
that the standard definition of fairness often is unnecessarily weak and can be
replaced by the stronger, yet still abstract, notion of finitary fairness. While
standard weak fairness requires that no enabled transition is postponed forever,
finitary weak fairness requires that for every run of a system there is an unknown
bound k such that no enabled transition is postponed more than k consecutive times.
In general, the finitary restriction fin(F) of any given fairness assumption F
is the union of all w-regular safety properties that are contained in F. The adequacy
of the proposed abstraction is demonstrated in two ways. Suppose that we prove
a program property under the assumption of finitary fairness. In a multiprogramming
environment, the program then satisfies the property for all fair finite-state
schedulers. In a distributed environment, the program then satisfies the property
for all choices of lower and upper bounds on the speeds (or timings) of processors'
article_processing_charge: No
author:
- first_name: Rajeev
full_name: Alur, Rajeev
last_name: Alur
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
citation:
ama: 'Alur R, Henzinger TA. Finitary fairness. In: Proceedings 9th Annual IEEE
Symposium on Logic in Computer Science. IEEE; 1994:52-61. doi:10.1109/LICS.1994.316087 '
apa: 'Alur, R., & Henzinger, T. A. (1994). Finitary fairness. In Proceedings
9th Annual IEEE Symposium on Logic in Computer Science (pp. 52–61). Paris,
France: IEEE. https://doi.org/10.1109/LICS.1994.316087
'
chicago: Alur, Rajeev, and Thomas A Henzinger. “Finitary Fairness.” In Proceedings
9th Annual IEEE Symposium on Logic in Computer Science, 52–61. IEEE, 1994.
https://doi.org/10.1109/LICS.1994.316087
.
ieee: R. Alur and T. A. Henzinger, “Finitary fairness,” in Proceedings 9th Annual
IEEE Symposium on Logic in Computer Science, Paris, France, 1994, pp. 52–61.
ista: 'Alur R, Henzinger TA. 1994. Finitary fairness. Proceedings 9th Annual IEEE
Symposium on Logic in Computer Science. LICS: Logic in Computer Science, 52–61.'
mla: Alur, Rajeev, and Thomas A. Henzinger. “Finitary Fairness.” Proceedings
9th Annual IEEE Symposium on Logic in Computer Science, IEEE, 1994, pp. 52–61,
doi:10.1109/LICS.1994.316087
.
short: R. Alur, T.A. Henzinger, in:, Proceedings 9th Annual IEEE Symposium on Logic
in Computer Science, IEEE, 1994, pp. 52–61.
conference:
end_date: "\t1994-07-07"
location: Paris, France
name: 'LICS: Logic in Computer Science'
start_date: 1994-07-04
date_created: 2018-12-11T12:09:37Z
date_published: 1994-01-01T00:00:00Z
date_updated: 2022-06-02T08:45:57Z
day: '01'
doi: '10.1109/LICS.1994.316087 '
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://ieeexplore.ieee.org/document/316087
month: '01'
oa_version: None
page: 52 - 61
publication: Proceedings 9th Annual IEEE Symposium on Logic in Computer Science
publication_identifier:
issn:
- 0018-9162
publication_status: published
publisher: IEEE
publist_id: '119'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Finitary fairness
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
year: '1994'
...
---
_id: '4596'
abstract:
- lang: eng
text: A real-time temporal logic for the specification of reactive systems is introduced.
The novel feature of the logic, TPTL, is the adoption of temporal operators as
quantifiers over time variables; every modality binds a variable to the time(s)
it refers to. TPTL is demonstrated to be both a natural specification language
and a suitable formalism for verification and synthesis. A tableau-based decision
procedure and model-checking algorithm for TPTL are presented. Several generalizations
of TPTL are shown to be highly undecidable.
acknowledgement: 'We thank Zohar Manna, Amir Pnueli, and David Dill for their guidance.
Moshe Vardi and Joe Halpern gave us very helpful advice for refilling our undecidability
results. '
article_processing_charge: No
author:
- first_name: Rajeev
full_name: Alur, Rajeev
last_name: Alur
- first_name: Thomas A
full_name: Henzinger, Thomas A
id: 40876CD8-F248-11E8-B48F-1D18A9856A87
last_name: Henzinger
orcid: 0000−0002−2985−7724
citation:
ama: 'Alur R, Henzinger TA. A really temporal logic. In: 30th Annual Symposium
on Foundations of Computer Science. FCOS. IEEE; 1989:164-169. doi:10.1109/SFCS.1989.63473'
apa: 'Alur, R., & Henzinger, T. A. (1989). A really temporal logic. In 30th
Annual Symposium on Foundations of Computer Science (pp. 164–169). Research
Triangle Park, NC, USA: IEEE. https://doi.org/10.1109/SFCS.1989.63473'
chicago: Alur, Rajeev, and Thomas A Henzinger. “A Really Temporal Logic.” In 30th
Annual Symposium on Foundations of Computer Science, 164–69. FCOS. IEEE, 1989.
https://doi.org/10.1109/SFCS.1989.63473.
ieee: R. Alur and T. A. Henzinger, “A really temporal logic,” in 30th Annual
Symposium on Foundations of Computer Science, Research Triangle Park, NC,
USA, 1989, pp. 164–169.
ista: 'Alur R, Henzinger TA. 1989. A really temporal logic. 30th Annual Symposium
on Foundations of Computer Science. FOCS: Foundations of Computer ScienceFCOS,
164–169.'
mla: Alur, Rajeev, and Thomas A. Henzinger. “A Really Temporal Logic.” 30th Annual
Symposium on Foundations of Computer Science, IEEE, 1989, pp. 164–69, doi:10.1109/SFCS.1989.63473.
short: R. Alur, T.A. Henzinger, in:, 30th Annual Symposium on Foundations of Computer
Science, IEEE, 1989, pp. 164–169.
conference:
end_date: 1989-11-01
location: Research Triangle Park, NC, USA
name: 'FOCS: Foundations of Computer Science'
start_date: 1989-10-30
date_created: 2018-12-11T12:09:40Z
date_published: 1989-01-01T00:00:00Z
date_updated: 2022-02-09T10:40:13Z
day: '01'
doi: 10.1109/SFCS.1989.63473
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://ieeexplore.ieee.org/document/63473
month: '01'
oa_version: None
page: 164 - 169
publication: 30th Annual Symposium on Foundations of Computer Science
publication_identifier:
eissn:
- 1558-0814
isbn:
- 0-8186-1982-1
issn:
- 0018-9162
publication_status: published
publisher: IEEE
publist_id: '111'
quality_controlled: '1'
series_title: FCOS
status: public
title: A really temporal logic
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
year: '1989'
...
---
_id: '4128'
abstract:
- lang: eng
text: A generalization of the convex hull of a finite set of points in the plane
is introduced and analyzed. This generalization leads to a family of straight-line
graphs, " \alpha -shapes," which seem to capture the intuitive notions of "fine
shape" and "crude shape" of point sets. It is shown that a-shapes are subgraphs
of the closest point or furthest point Delaunay triangulation. Relying on this
result an optimal O(n \log n) algorithm that constructs \alpha -shapes is developed.
acknowledgement: "The authors express their appreciation for numerous constructive
suggestions, which led to improvements on\r\nvarious phases of the manuscript, to
Dr. Marvin Simon of JPL and to Professor George L. Turin of University of\r\nCalifornia,
Berkeley. The junior author also gratefully acknowledges the role of the latter
as her M.S. research\r\nadvisor on the project which formed the nucleus of this
work. \r\n"
article_processing_charge: No
article_type: original
author:
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: David
full_name: Kirkpatrick, David
last_name: Kirkpatrick
- first_name: Raimund
full_name: Seidel, Raimund
last_name: Seidel
citation:
ama: Edelsbrunner H, Kirkpatrick D, Seidel R. On the shape of a set of points in
the plane. IEEE Transactions on Information Theory. 1983;29(4):551-559.
doi:10.1109/TIT.1983.1056714
apa: Edelsbrunner, H., Kirkpatrick, D., & Seidel, R. (1983). On the shape of
a set of points in the plane. IEEE Transactions on Information Theory.
IEEE. https://doi.org/10.1109/TIT.1983.1056714
chicago: Edelsbrunner, Herbert, David Kirkpatrick, and Raimund Seidel. “On the Shape
of a Set of Points in the Plane.” IEEE Transactions on Information Theory.
IEEE, 1983. https://doi.org/10.1109/TIT.1983.1056714
.
ieee: H. Edelsbrunner, D. Kirkpatrick, and R. Seidel, “On the shape of a set of
points in the plane,” IEEE Transactions on Information Theory, vol. 29,
no. 4. IEEE, pp. 551–559, 1983.
ista: Edelsbrunner H, Kirkpatrick D, Seidel R. 1983. On the shape of a set of points
in the plane. IEEE Transactions on Information Theory. 29(4), 551–559.
mla: Edelsbrunner, Herbert, et al. “On the Shape of a Set of Points in the Plane.”
IEEE Transactions on Information Theory, vol. 29, no. 4, IEEE, 1983, pp.
551–59, doi:10.1109/TIT.1983.1056714
.
short: H. Edelsbrunner, D. Kirkpatrick, R. Seidel, IEEE Transactions on Information
Theory 29 (1983) 551–559.
date_created: 2018-12-11T12:07:06Z
date_published: 1983-06-01T00:00:00Z
date_updated: 2022-01-25T12:55:07Z
day: '01'
doi: '10.1109/TIT.1983.1056714 '
extern: '1'
intvolume: ' 29'
issue: '4'
language:
- iso: eng
main_file_link:
- url: https://ieeexplore.ieee.org/document/1056714
month: '06'
oa_version: None
page: 551 - 559
publication: IEEE Transactions on Information Theory
publication_identifier:
eissn:
- 1558-0814
issn:
- 0018-9162
publication_status: published
publisher: IEEE
publist_id: '1995'
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the shape of a set of points in the plane
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 29
year: '1983'
...